If this AI is at all close to what humans are like (again it is a mildly friendly AI) it will become paranoid about the possibility that there's some similar programming issue in it"

AI would notice it anyway. Given some broken enough design it might be unable to care about that flaw, but if that's the case, it won't go paranoid over it. It just doesn't care.

Of course, if we break the design even more, we might get an AI that tries to combine unified theory of physics with the "fact" that red wire actually doesn't kill itself, results of that would probably be worth their own comic series. That sort of AI then again is probably broken enough to be next to useless, but still extremely dangerous piece of computing power. It would probably explode hilariously too if it could understand the analogy between itself and the crippled AI we're discussing here, and actually care about that.